ABSTRACT Cerebellar processing is associated with the accurate performance of a range of behaviors, from sensorimotor transformations to executive control. Given this wide range, there is remarkable consistency across modality and species in the organization of cerebellar microcircuitry and the closed-loop manner with which cerebellar regions are connected to other brain areas. This consistency suggests a common computational role, which we hypothesize is most generally described as an adaptive temporal filter. To test this hypothesis, we will investigate cerebellar function in a simple motor plasticity, the learning of fixation stability. In this setting, processing as an adaptive filter should be realized as a capacity in the cerebellum to alternatively act as a proportional, integrating, or differentiating gain element. In Aim 1, cerebellar filtering will be assessed by using two-photon calcium imaging in the larval zebrafish to measure activity at both input granule and output Purkinje cells populations. Adaptation of the filter will be determined by measuring changes in the relationship between input and output neurons as fixations are trained toward greater or lesser stability. In Aim 2, computational models of the cerebellum will be constructed that generate the experimentally measured signal transformation and make predictions about the mechanisms of cerebellar filtering. These predictions will be tested by focal stimulation of granule cells and measurement of resultant Purkinje neuron responses. Together these data promise to generate the most complete understanding to date of the cerebellum's computational importance in behavior.